- published: 02 Dec 2012
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The standard error is the standard deviation of the sampling distribution of a statistic. The term may also be used to refer to an estimate of that standard deviation, derived from a particular sample used to compute the estimate.
For example, the sample mean is the usual estimator of a population mean. However, different samples drawn from that same population would in general have different values of the sample mean. The standard error of the mean (i.e., of using the sample mean as a method of estimating the population mean) is the standard deviation of those sample means over all possible samples (of a given size) drawn from the population. Secondly, the standard error of the mean can refer to an estimate of that standard deviation, computed from the sample of data being analyzed at the time.
A way for remembering the term standard error is that, as long as the estimator is unbiased, the standard deviation of the error (the difference between the estimate and the true value) is the same as the standard deviation of the estimates themselves; this is true since the standard deviation of the difference between the random variable and its expected value is equal to the standard deviation of a random variable itself.
Standard Error
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